Real‐time anomaly detection with Bayesian dynamic linear models

A key goal in Structural Health Monitoring is to detect abnormal events in a structure’s behavior by interpreting its observed responses over time. The goal is to develop an anomaly-detection method that (i) is robust towards false alarm, and (ii) capable of performing real-time analysis. The majority of anomaly detection approaches are currently operating over batches of data for which the model parameters are assumed to be constant over time, and to be equal to the values estimated during a fixed-size training-period. This assumption is not suited for the real-time anomaly detection where model parameters need to be treated as time-varying quantities. This paper presents how this issue is tackled by combining Rao-Blackwellized Particle Filtering (RBPF) with the Bayesian Dynamic Linear Models (BDLMs). The BDLMs, which is a special case of state space models, allow decomposing time-series into a vector of hidden state variables. The RBPF employs the sequential Monte Carlo method to learn model parameters continuously as the new observations are collected. The potential of the new approach is illustrated on the displacement data collected from a dam in Canada. The approach succeeds in detecting the anomaly caused by the refection work on the dam as well as the artificial anomalies that are introduced on the original dataset. The new method opens the way for monitoring the structure’s health and conditions in real-time.

[1]  David S. Ebert,et al.  Spatiotemporal social media analytics for abnormal event detection and examination using seasonal-trend decomposition , 2012, 2012 IEEE Conference on Visual Analytics Science and Technology (VAST).

[2]  Michael A. West,et al.  Combined Parameter and State Estimation in Simulation-Based Filtering , 2001, Sequential Monte Carlo Methods in Practice.

[3]  Jouko Lampinen,et al.  Rao-Blackwellized particle filter for multiple target tracking , 2007, Inf. Fusion.

[4]  A. Emin Aktan,et al.  Structural identification of constructed systems : approaches, methods, and technologies for effective practice of St-Id , 2013 .

[5]  James-A. Goulet.  Bayesian dynamic linear models for structural health monitoring , 2017 .

[6]  Andrew W. Smyth,et al.  Particle filtering and marginalization for parameter identification in structural systems , 2017 .

[7]  Jerome P. Lynch,et al.  A summary review of wireless sensors and sensor networks for structural health monitoring , 2006 .

[8]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[9]  Eyal Amir,et al.  Real-time Bayesian Anomaly Detection for Environmental Sensor Data , 2007 .

[10]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[11]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[12]  Christopher Nemeth,et al.  Sequential Monte Carlo Methods for State and Parameter Estimation in Abruptly Changing Environments , 2014, IEEE Transactions on Signal Processing.

[13]  Ryan P. Adams,et al.  Bayesian Online Changepoint Detection , 2007, 0710.3742.

[14]  M. Hoshiya,et al.  Structural Identification by Extended Kalman Filter , 1984 .

[15]  A.R. Runnalls,et al.  A Kullback-Leibler Approach to Gaussian Mixture Reduction , 2007 .

[16]  Francesco Cadini,et al.  A particle filter‐based model selection algorithm for fatigue damage identification on aeronautical structures , 2017 .

[17]  James-A. Goulet,et al.  Anomaly detection with the Switching Kalman Filter for structural health monitoring , 2018 .

[18]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[19]  Philip S. Yu,et al.  A Framework for Clustering Evolving Data Streams , 2003, VLDB.

[20]  Eleni Chatzi,et al.  Particle filter scheme with mutation for the estimation of time‐invariant parameters in structural health monitoring applications , 2013 .

[21]  Subutai Ahmad,et al.  Unsupervised real-time anomaly detection for streaming data , 2017, Neurocomputing.

[22]  Lovekesh Vig,et al.  Long Short Term Memory Networks for Anomaly Detection in Time Series , 2015, ESANN.

[23]  Kevin Murphy,et al.  Switching Kalman Filters , 1998 .

[24]  Yuwei Cui,et al.  Continuous Online Sequence Learning with an Unsupervised Neural Network Model , 2015, Neural Computation.

[25]  Wolfram Burgard,et al.  Fast and accurate SLAM with Rao-Blackwellized particle filters , 2007, Robotics Auton. Syst..

[26]  Maciej Szmit,et al.  Usage of Modified Holt-Winters Method in the Anomaly Detection of Network Traffic: Case Studies , 2012, J. Comput. Networks Commun..

[27]  Siem Jan Koopman,et al.  Time Series Analysis by State Space Methods , 2001 .

[28]  J. Yosinski,et al.  Time-series Extreme Event Forecasting with Neural Networks at Uber , 2017 .

[29]  David A. Clifton,et al.  A review of novelty detection , 2014, Signal Process..

[30]  Wolfram Burgard,et al.  Improving Grid-based SLAM with Rao-Blackwellized Particle Filters by Adaptive Proposals and Selective Resampling , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[31]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.

[32]  James-A. Goulet,et al.  A Kernel-Based Method for Modeling Non-harmonic Periodic Phenomena in Bayesian Dynamic Linear Models , 2019, Front. Built Environ..

[33]  Shai Ben-David,et al.  Detecting Change in Data Streams , 2004, VLDB.

[34]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[35]  Andrew W. Smyth,et al.  On the Performance of Online Parameter Estimation Algorithms in Systems with Various Identifiability Properties , 2017, Front. Built Environ..

[36]  Ka-Veng Yuen,et al.  Stable Robust Extended Kalman Filter , 2017 .

[37]  Terrence J. Sejnowski,et al.  Parallel Networks that Learn to Pronounce English Text , 1987, Complex Syst..

[38]  Sudipto Guha,et al.  Robust Random Cut Forest Based Anomaly Detection on Streams , 2016, ICML.

[39]  James-A. Goulet,et al.  Uncertainty quantification for model parameters and hidden state variables in Bayesian dynamic linear models , 2018, Structural Control and Health Monitoring.

[40]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[41]  A. Emin Aktan,et al.  On Structural Identification of Constructed Facilities , 1996 .

[42]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[43]  Ka-Veng Yuen,et al.  Real‐time substructural identification by boundary force modeling , 2018 .

[44]  Simo Särkkä,et al.  Bayesian Filtering and Smoothing , 2013, Institute of Mathematical Statistics textbooks.

[45]  James-A. Goulet,et al.  Structural Health Monitoring with dependence on non-harmonic periodic hidden covariates , 2018, Engineering Structures.